Scalar potentials of this form have received considerable attention in the past (see for instance [1]}, [2]}, [3]}), and we review here some standard steps. To find the lowest energy state of the potential, we work in the unitary gauge and expand both fields about their vacuum expectation values (VEVs), denoted by \( v_H \)  and \( v_{\theta }\) :
\(H =\begin{pmatrix}0 \\\frac{v_H + h^{\prime }}{\sqrt{2}} \\\end{pmatrix},\qquad \theta = \frac{v_{\theta } + \vartheta ^{\prime }}{\sqrt{2}}.\) 
